A Bayesian Exploration on Scooby Doo Villain Unmasking

Does the villain’s motive impact the likelihood of successful capture in Scooby Doo episodes?

Curtis, RK, Hooman, Johnny

Fear Prior Distribution

  • Rationale:
    Fear is not confident about the probability of unmasking, so \(\pi\) can be set as \(0.50\). Considering Fear is not confident about his answer, the his distribution will have a wide shape, large variance. We picked \(\alpha = 2\) and \(\beta=2\) such that \(\pi=0.50\) and \(V[\pi]=0.50\), based on the beta distribution expectation: \(E[\pi]= \frac{\alpha}{\alpha + \beta}\)

Ennui Prior Distribution

  • Rationale:
    Ennui shrugs when asked each question, which means that there is not much information from her. That is, we are uncertain about her thought about \(\pi\).

Joy Prior Distribution

  • Rationale:
    Joy is very certain about the unmasking, and very confident about her answer, so I set the expectation of \(\pi\) to \(0.90\) by setting \(\alpha=9\) and \(\beta=1\).

Villian Motive Theft: Fear Iteration


Villian Motive Theft: Ennui Iteration


Villian Motive Theft: Joy Iteration

Prior and motive impact on the posterior: Villian Motive Theft

Villian Motive Competition

Summary of Competition Motive Episodes:

decade Unmasked_No Unmasked_Yes n_episodes
1960s 1 3 4
1970s 8 8 16
1980s 14 10 24
1990s 0 4 4
2000s 16 24 40
2010s 19 51 70
2020s 2 8 10

Fear Prior’s and Posteriors for Competition Motive Episodes:

decade prior posterior emotion
1960s Beta(2,2) Beta(5,3) Fear
1970s Beta(5,3) Beta(13,11) Fear
1980s Beta(13,11) Beta(23,25) Fear
1990s Beta(23,25) Beta(27,25) Fear
2000s Beta(27,25) Beta(51,41) Fear
2010s Beta(51,41) Beta(102,60) Fear
2020s Beta(102,60) Beta(110,62) Fear

Joy Prior’s and Posteriors for Competition Motive Episodes:

decade prior posterior emotion
1960s Beta(9,1) Beta(12,2) Joy
1970s Beta(12,2) Beta(20,10) Joy
1980s Beta(20,10) Beta(30,24) Joy
1990s Beta(30,24) Beta(34,24) Joy
2000s Beta(34,24) Beta(58,40) Joy
2010s Beta(58,40) Beta(109,59) Joy
2020s Beta(109,59) Beta(117,61) Joy

Ennui Prior’s and Posteriors for Competition Motive Episodes:

decade prior posterior emotion
1960s Beta(1,1) Beta(4,2) Ennui
1970s Beta(4,2) Beta(12,10) Ennui
1980s Beta(12,10) Beta(22,24) Ennui
1990s Beta(22,24) Beta(26,24) Ennui
2000s Beta(26,24) Beta(50,40) Ennui
2010s Beta(50,40) Beta(101,59) Ennui
2020s Beta(101,59) Beta(109,61) Ennui

Evolution of the posteriors of all 3 emotions in Competition Motive Episodes over the decades:

Villian Motive Power

Villian Motive Power: Fear Iteration

Villian Motive Power: Ennui Iteration

Villian Motive Power: Joy Iteration

Prior and motive impact on the posterior: Villian Motive Power

Villian Motive Greed

Johnny

Summary